The United States cranked up the pressure on Venezuela's President Nicolas Maduro on Tuesday, imposing sanctions on his wife and more of his inner circle and issuing harsh warnings about his vulnerability to an overthrow.

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President Donald Trump said the "repressive regime" in Caracas that is responsible for a "human tragedy" in the once oil-rich nation "could be toppled very quickly by the military if the military decides to do that."

But he declined to talk about possible US military options.

"I don't like to talk about military.... I'm not going to tell," Trump said during a meeting with the president of Venezuela's neighbor Colombia, on the sidelines of the United Nations General Assembly.

The issue is even more sensitive given a New York Times report this month saying Trump administration officials had met three times with Venezuelan military officers to discuss plans to oust Maduro but the plans stalled.

"Currently we are witnessing the human tragedy" in Venezuela, Trump told world leaders gathered at the United Nations. "More than two million people have fled the anguish inflicted by the socialist Maduro regime and its Cuban sponsors."

New sanctions

The US Treasury earlier Tuesday announced new sanctions against Venezuelan first lady Cilia Adela Flores de Maduro, a former attorney general and the president's wife, as one of the figures who has helped Maduro retain his grip on power, along with Vice President Delcy Rodriguez.

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He said Maduro's socialism "has bankrupted the oil-rich nation and driven its people into abject poverty."

Maduro slammed the US move against his wife as cowardly.

"Don't mess with Cilia. Don't mess with family. Don't be cowards!" Maduro fumed during a televised event, warning that his wife would not be cowed "because Cilia is a fierce woman."

Meanwhile, Canada's Foreign Minister Chrystia Freeland said the situation in Venezuela "is one of our foreign policy priorities," and Ottawa is urging action to help with the growing refugee crisis and its impact on neighboring Colombia.

The "migration crisis coming out of Venezuela is not just a local problem, it has to be a problem for our hemisphere and really a global problem," Freeland said at an event on the sidelines of the UN assembly.

"There are a lot of people who are fleeing Venezuela, and these people, in addition to being poor and hungry, many of them are really sick and have illnesses which we thought had been eradicated."

She also said sanctions against the regime are needed.

"The Venezuelan leadership needs to know that actions have consequences," Freeland said. "And all of us need to continue to let the people of Venezuela know that they have our support."

'Tragic decline'

The other Venezuelan officials US Treasury targeted with sanctions were described as members of Maduro's inner circle -- Communications Minister Jorge Rodriguez and Defense Minister Vladimir Padrino Lopez.

"Treasury will continue to impose a financial toll on those responsible for Venezuela's tragic decline and the networks and front-men they use to mask their illicit wealth," US Treasury Secretary Steven Mnuchin said in a statement.

Those hit with sanctions will have any assets or property in the United States seized -- including a Gulfstream 200 private jet located in Florida and owned by Rafael Sarria Diaz, named as a front man -- and US institutions are prohibited from doing business with them.

Maduro already was hit with the same penalties on July 31, 2017, as was Diosdado Cabello, president of Venezuela's National Constituent Assembly (ANC).

Treasury said the sanctions could be lifted if the officials "take concrete and meaningful actions to restore democratic order, refuse to take part in human rights abuses, speak out against abuses committed by the government, and combat corruption in Venezuela."

Some 2.3 million Venezuelans, or 7.5 percent of the population, live abroad with the number sharply growing in the past several years as hyperinflation slashes the worth of salaries and makes necessities prohibitively expensive, according to the UN.

The collapse of Venezuela's oil-based economy under the increasingly authoritarian Maduro has led to dire shortages of food and medicine.